|
|
|
Some new generating function formulae of the two-variable Hermite polynomials and their application in quantum optics |
| Zhan De-Hui (展德会)a b, Fan Hong-Yi (范洪义)a |
a Department of Material Science and Engineering, University of Science and Technology of China, Hefei 230026, China;
b College of Mechanic and Electronic Engineering, Wuyi University, Wuyishan 354300, China |
|
|
|
|
Abstract We derive some new generating function formulae of the two-variable Hermite polynomials, such as .jpg) , .jpg) , and .jpg) . We employ the operator Hermite polynomial method and the technique of integration within an ordered product of operators to solve these problems, which will be useful in constructing new optical field states.
|
Received: 01 April 2014
Revised: 23 June 2014
Accepted manuscript online:
|
|
PACS:
|
03.65.-w
|
(Quantum mechanics)
|
| |
02.30.Gp
|
(Special functions)
|
|
| Fund: Project supported by the National Natural Science Foundation of China (Grnat No. 11175113) and the Fundamental Research Funds for the Central Universities of China (Grant No. WK2060140013). |
Corresponding Authors:
Zhan De-Hui
E-mail: dhzhan@mail.ustc.edu.cn
|
Cite this article:
Zhan De-Hui (展德会), Fan Hong-Yi (范洪义) Some new generating function formulae of the two-variable Hermite polynomials and their application in quantum optics 2014 Chin. Phys. B 23 120301
|
| [1] |
Fan H Y and Zhan D H 2014 Chin. Phys. B 23 060301
|
| [2] |
Fan H Y and Jiang T F 2007 Mod. Phys. Lett. B 21 475
|
| [3] |
Erdelyi A 1953 Higher Transcendental Functions (The Bateman Manuscript Project)
|
| [4] |
Yuan H C, Li H M and Xu X F 2013 Chin. Phys. B 22 060301
|
| [5] |
Fan H Y, Zhan D H, Yu W J and Zhou J 2012 Acta Phys. Sin. 61 110302 (in Chinese)
|
| [6] |
Yang Y and Fan H Y 2013 Chin. Phys. B 22 020303
|
| [7] |
Fan H Y and Tang X B 2008 Devolopment of Basis of the Mathematical Physics of Quantum Mechanics (Hefei: University of Science and Technology of China Press) p. 38
|
| [8] |
Ozaktas H M and Mendlovic D 1993 Opt. Commun. 101 163
|
| [9] |
Fan H Y and Li X C 2012 Acta Phys. Sin. 61 200301 (in Chinese)
|
| [10] |
Fan H Y 2012 Representation and Transformation Theory in Quantum Mechanics: Dirac's Symbolic Method, 2nd edn. (Hefei: University of Science and Technology Press) p. 269
|
| [11] |
Fan H Y and Wang Z 2014 Chin. Phys. B 23 080301
|
| [12] |
Fan, H Y, Xu X X and Hu L Y 2010 Chin. Phys. B 19 060502
|
| [13] |
Fan H Y, He R, Da C and Liang Z F 2013 Chin. Phys. B 22 080301
|
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
